The numerical results with full grid and sparse grid for \(k=1,2,3\)  are shown in Table REF  and Table REF , respectively. We observe clearly \((k+1)\)  order of accuracy for full grid, which verifies our optimal error estimate in Theorem REF . Moreover, slightly more than \((k+\frac{1}{2})\)  order of accuracy is observed for sparse grid, which is consistent with approximation results for sparse grid, e.g. see [1]} for results on elliptic equations.
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